Sr Examen
Integral de 1/(sqrt(1/(x^2)-1)) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------- dx | ________ | / 1 | / -- - 1 | / 2 | \/ x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{-1 + \frac{1}{x^{2}}}}\, dx$$
Integral(1/(sqrt(1/(x^2) - 1)), (x, 0, 1))
Respuesta (Indefinida)
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/ // _________ \ | || / 2 | 2| | | 1 ||-I*\/ -1 + x for |x | > 1| | ------------- dx = C + |< | | ________ || ________ | | / 1 || / 2 | | / -- - 1 \\ -\/ 1 - x otherwise / | / 2 | \/ x | /
$$\int \frac{1}{\sqrt{-1 + \frac{1}{x^{2}}}}\, dx = C + \begin{cases} - i \sqrt{x^{2} - 1} & \text{for}\: \left|{x^{2}}\right| > 1 \\- \sqrt{1 - x^{2}} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
1 / | | / -I*x 2 | |------------ for x > 1 | | _________ | | / 2 | |\/ -1 + x | < dx | | x | |----------- otherwise | | ________ | | / 2 | \\/ 1 - x | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{x^{2} - 1}} & \text{for}\: x^{2} > 1 \\\frac{x}{\sqrt{1 - x^{2}}} & \text{otherwise} \end{cases}\, dx$$
=
=
1 / | | / -I*x 2 | |------------ for x > 1 | | _________ | | / 2 | |\/ -1 + x | < dx | | x | |----------- otherwise | | ________ | | / 2 | \\/ 1 - x | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{x^{2} - 1}} & \text{for}\: x^{2} > 1 \\\frac{x}{\sqrt{1 - x^{2}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-i*x/sqrt(-1 + x^2), x^2 > 1), (x/sqrt(1 - x^2), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.